Practice Problems 1 TIMBER DESIGNCLOSED NOTES, HANDOUTS, BOOKS AND HOMEWORKS *Read problems completely and carefully before beginning to solve. Name:_______________________________________ School ID No.:_______________ Section: _________________ 75 I. Multiple Choice ( 1.5 points each) Instruction: Solved the following problems and write the corresponding letter of your answer on the space provided in the separate answer sheet provided. SITUATION 1 See figureTD-FE001. Beam AB is simply supported at A and is fixed at B. Column AC is 200 mm square timber with the following properties: Allowable stresses: Bending and tension parallel to the grain = 21.8 MPa; Compression parallel to the grain = 13.2 MPa Shear parallel to the grain = 2.40 MPa; Compression perpendicular to the grain = 4.26 MPa Modulus of elasticity = 8.47 GPa Use: H = 6 m; L=8m Problem 1 What is the allowable concentric load (kN) in column AC if both ends are pin-connected? Sidesway is prevented. Assume Ke = 1.0. a. 113 b. 528 c. 354 d. 165 Problem 2 Determine the moment capacity (kN.m) of beam AB, if its dimensions and properties are the same in column AC. a. 27.79 b. 29.07 c. 28.19 d. 64.41 Problem 3 Calculate the safe uniform load (kN/m) including its own weight for beam AB. a. 3.63 b. 3.47 c. 3.52 d. 8.05 SITUATION 2 See figureTD-FE002. The wooden member shown, a = 50 mm, b = 75 mm in cross section is subjected to a load P =200 kN. The plane AA makes an angle 15º with the x-axis. Problem 4 What is the tensile stress at section A-A in MPa? a. 53.33 b. 51.52 c. 49.76 d. 13.33 Problem 5 Determine the shear stress on plane A-A in MPa? a. 3.43 b. 51.52 c. 49.76 d. 13.33 Problem 6 At what angle of plane A-A is the shear stress maximum, degrees? a. 15 b. 30 c. 45 d. 90 SITUATION 3 See figureTD-FE003. Wooden posts having diameters of 300 mm are used to support the electrical cables shown acting as approximately parabolic cables. The height of the posts is 10 m and spaced at 60 m. The properties of the wood are: Allowable stresses: Bending and tension parallel to the grain = 21.8 MPa; Compression parallel to the grain = 13.2 MPa Shear parallel to the grain = 2.40 MPa; Compression perpendicular to the grain = 4.26 MPa Modulus of elasticity = 8.47 GPa Assume Ke = 1.2 Problem 7 Determine the allowable uniform weight of the electrical cables (in kN/m) with a maximum sag of 1 m. a. 1.47 b. 15.55 c. 14.55 d. 4.99 Problem 8 Calculate the moment capacity of the posts, in kN.m. a. 68.28 b. 67.37 c. 44.17 d. 66.87 Problem 9 Compute the allowed horizontal tension at one side on top of the posts if the weight of the cables is 0.5 kN/m. a. 4.42 b. 15.00 c. 225.00 d. 6.83 1|Page Practice Problems 1 TIMBER DESIGN SITUATION 4 A log that is 600 mm in diameter is to be cut into a rectangular section for use as a simply supported beam. A concentrated load P = 507 kN is applied at midspan. If the allowable bending stress for the wood is 55 MPa. Problem 10 If the width of the beam is 200 mm, by geometry what is the depth of the beam, in mm? a. 471.24 b. 535.30 c. 565.69 d. 565.49 Problem 11 If the depth of the beam is 500 mm, determine the required width (in mm) so that the stress will not exceed the allowable bending stress. a. 267.65 b. 271.01 c. 282.84 d. 471.24 Problem 12 Determine the amount of waste in board foot in the construction of the beam. a. 63 b. 94 c. 275 d. 306 SITUATION 5 A square 250 mm vertical wooden post is embedded in a concrete foundation and held at the top by two cables (see figure TD-FE004). Use Ke = 2.1 Allowable stresses: Bending and tension parallel to the grain = 16.5 MPa; Compression parallel to the grain = 10.5 MPa Shear parallel to the grain = 2.71 MPa; Compression perpendicular to the grain = 3.83 MPa Modulus of elasticity = 4.66 GPa Use: b = 2 m; h=2m What is the maximum allowable tensile force Tallow (in kN) in the cables, if: Problem 13 The wooden post is a short column a. 218.90 b. 464.04 c. 155.45 d. 309.58 Problem 14 The wooden post is a intermediate column a. 218.90 b. 464.04 c. 155.45 d. 309.58 Problem 15 The wooden post is a slender column a. 218.90 b. 464.04 c. 155.45 d. 309.58 SITUATION 6 A small dam of height h = 2.5 m is constructed of vertical wood beams, as shown in the figure TD-FE005. The wood beams, which have thickness t = 100 mm are simply supported by horizontal steel beams at A and B. Problem 16 Calculate the maximum bending stress if the depth of water is 2.0 m, in MPa. a. 4.09 b. 3.89 c. 3.99 d. 3.73 Problem 17 Compute the maximum shear stress if the depth of water is 2.0 m, in MPa. a. 0.19 b. 0.31 c. 0.25 d. 0.22 Problem 18 Compute the maximum depth of water if the allowable bending stress is 3.5 MPa, in m. a. 1.52 b. 1.31 c. 1.94 d. 1.42 SITUATION 7 A 80% stress grade Apitong beam 250 mm x 425 mm has a simple span of 8 m. Use: Fb (bending) = 16.5 MPa; Fv (shear) = 1.73 MPa; Ew = 7.31 GPa; Sp.gr = 0.57 Problem 19 Which of the following gives the size factor? a. 0.962 b. 0.840 c. 1.022 d. 0.965 Problem 20 Which of the following gives the safe uniform load including its weight (in kN/m) that the beam could support based on the flexural stress with size factor adjustment? a. 12.45 b. 14.26 c. 14.34 d. 14.93 Problem 21 Which of the following gives the safe uniform load excluding its weight (in kN/m) that the beam could support based on the allowable shearing stress? a. 30.04 b. 30.64 c. 45.36 d. 68.34 2|Page Practice Problems 1 TIMBER DESIGN SITUATION 8 Determine the flexural strength (in kN.m) of an 12 m simply supported floor joists 200 mm x 450 mm carrying uniform load throughout its span. Use Fb = 13.9 MPa and Ew = 5830 MPa Problem 22 If the beam is continuously supported laterally. a. 86.92 b. 66.21 c. 93.83 d. 89.69 Problem 23 If the beam is braced at midpoint. a. 66.21 b. 89.69 c. 86.92 d. 93.83 Problem 24 If the beam is braced at the ends. a. 66.21 b. 66.50 c. 66.21 d. 93.83 SITUATION 9 A cantilever beam having a span of 8 m has a cross-section of 150 mm x 450 mm at supports. It carries a uniformly distributed load w = 6 kN/m throughout its span. The beam is made up of visually stress-graded unseasoned Apitong with 80% stress grade with an allowable bending stress of 16.5 MPa and the allowable shear stress is 1.73 MPa. See figure TD- FE006. Neglect any adjustment on the bending stress. Problem 25 If the length of notching is 4 m, compute the minimum depth of the beam (in mm) at notched point, without exceeding the allowable stresses. a. 375.00 b. 337.50 c. 202.82 d. 341.12 Problem 26 If the depth of the beam at notched points is 200 mm, determine the length of notching “b” (in m) without exceeding its allowable bending strength. a. 2.35 b. 2.88 c. 4.69 d. 5.77 Problem 27 If the depth of the beam at notched point is 200 mm, and the length of notching is 3 m calculate the safe uniformly load (in kN/m) that the beam can carry without exceeding its allowable bending strength. a. 11.53 b. 3.67 c. 5.77 d. 7.33 SITUATION 10 A timber beam 150 mm wide by 300 mm deep is to be reinforced at the top and bottom by steel plates 12 mm thick. Assume that n = 10, the beam is to resist a moment of 60 kN.m. (see figure TD-FE007) Use: b (wood) = 150 mm; h = 300 mm; t = 12 mm Problem 28 Determine the width of the steel plates without exceeding the stress in the wood of 10 MPa and the stress of steel of 150 MPa, in mm? a. 50 b. 75 c. 100 d. 125 Problem 29 If the moment applied in the beam is 55 kN.m what is the maximum stress of wood, in MPa? a. 9.31 b. 8.95 c. 9.90 d. 9.67 Problem 30 If the moment applied in the beam is 55 kN.m what is the maximum stress of steel, in MPa? a. 89.49 b. 96.65 c. 93.07 d. 99.00 SITUATION 11 Refer to figure TD-FE008. Given: Span, L = 6.0 m Slope (Top chord) = 1V:4H Dead load = 1200 Pa (inclined) Wind Pressure Coefficients: Live load = 576 Pa (inclined) Windward side = 0.2 pressure Wind load = 2440 Pa Leeward side = 0.6 suction Properties of the Purlin b = 75 mm ; d = 225 mm Weight of wood = 5.59 kN/m3 Fb = Ft = 16.5 MPa; Ew = 7.31 GPa; p = 9.56 MPa; Fv = 1.75 MPa For D + L + W load combination, a one third increase in the allowable stresses is allowed. Problem 31 Find the safe purlin spacing (m) for D + L load combination. a. 0.5 b. 0.6 c. 0.7 d. 0.8 3|Page Practice Problems 1 TIMBER DESIGN Problem 32 Find the safe purlin spacing (m) for D + L + W where W is at the windward side. a. 0.6 b. 0.8 c. 1.0 d. 1.2 Problem 33 Find the safe purlin spacing (m) for D + L + W where W is at the leeward side. a. 1.0 b. 1.2 c. 1.3 d. 1.5 SITUATION 12 A palm tree weighing 4.45 kN is inclined at an angle of 60º (see TD-FE009). The weight of the tree may be resolved into two resultant forces, a force P1 = 4 kN acting at a point 3.6 m from the base and a force P2 = 0.45 kN acting at the top of the tree, which is 9.1 m long. The diameter at the base of the tree is 300 mm. Problem 34 Calculate the axial compressive in the palm tree, in kPa. a. 62.95 b. 31.48 c. 49.65 d. 54.52 Problem 35 Determine the maximum compressive stress in the palm tree, in kPa. a. 3,434.16 b. -6,074.04 c. -3,520.15 d. -3,543.20 Problem 36 Determine the maximum tensile stress in the palm tree, in kPa. a. 3,425.72 b. 3,434.16 c. 3,457.20 d. 6,074.04 SITUATION 13 The depth of notch of the joint shown equal to 50 mm. The bottom chord has a dimension of 75 mm x 200 mm while the diagonal member is 75 mm x 150 mm. The diagonal is subjected to an axial load of 30 kN at an angle of 25° with the bottom chord. See figure TD-FE010 Allowable compressive stresses are: Parallel to the grain = 8.3 MPa Perpendicular to the grain = 2.5 MPa Problem 37 Determine the angle that AB makes with the horizontal, in degrees. a. 20.91 b. 8.18 c. 12.50 d. 16.82 Problem 38 Compute the compressive stress of member BC, in MPa. a. 7.58 b. 7.43 c. 7.18 d. 7.84 Problem 39 Determine the allowable compressive stress of section AB, in MPa. a. 7.93 b. 5.44 c. 2.54 d. 5.87 SITUATION 14 A simply supported timber beam of rectangular cross section is reinforced by steel having an area of 4,800 mm2 at the bottom as shown in figure TD-FE011. In order to prevent corrosion in steel the reinforced beam is then wrap by structural fiber. The beam is to carry a maximum bending moment of 50 kN.m. Use n = 20 and the working bending stresses of 8 MPa for wood and 150 MPa for steel. Neglect the effect of the structural fibers. Use: d = 315 mm; h = 300 mm; b = 250 mm Problem 40 Determine the moment capacity of the wood without the steel reinforcement, in kN.m. a. 30.00 b. 6.00 c. 28.13 d. 56.25 Problem 41 Determine the moment capacity for composite action, in kN.m. a. 177.10 b. 34.28 c. 56.34 d. 33.14 Problem 42 Determine the percent increase in moment capacity. a. 46.75 b. 87.81 c. 14.27 d. 66.67 SITUATION 15 Refer to figure TD-FE016. The cross section of a narrow-gage railway bridge is shown in part (a) of the figure. The bridge is constructed with longitudinal steel girders that support the wood cross ties. The girders are restrained against lateral buckling by diagonal bracing, as indicated by the dashed lines. The spacing of the girders is S 1 = 1.5 m and the spacing of the rails is S2 = 1.0 m. The load transmitted by each rail to a single tie is P = 7.5 kN. The cross section of a tie, shown in part (b) of the figure, has width b = 150 mm and depth d. Allowable bending stress of 7.8 MPa in the wood tie. (Disregard the weight of the tie itself.) 4|Page Practice Problems 1 TIMBER DESIGN Problem 43 Calculate the maximum moment in the wood tie, in kN.m. a. 7.50 b. 0.94 c. 1.88 d. 3.75 3 Problem 44 Determine the required section modulus, in mm . a. 1.20 x 105 b. 9.62 x 105 c. 4.81 x 105 d. 2.40 x 105 Problem 45 Determine the minimum value of the depth d, in mm. a. 100 b. 75 c. 200 d. 150 Problem 46 A seesaw weighing 4 kg/m of length is occupied by two children, each weighing 35 kg (see figure TD-FE012). The center of gravity of each child is1.86 m from the fulcrum. The board is 5.8 m long, 200 mm wide. What is the required thickness (in inches) of the board if allowable bending stress in the board is 24.75 MPa? a. 1 ½ b. 1 ¼ c. 1 ¾ d. 2 Problem 47 A weight W = 22.10 kN falls through a height h = 2.0 mm onto the midpoint of a simple beam of length L = 4 m (see figure TD-FE013). The beam is made of wood with square cross section (dimension d on each side) and E = 12 GPa. If the allowable bending stress in the wood is σ allow = 10 MPa, what is the minimum required dimension d? Round-up your answer to the nearest 10 mm. a. 300 b. 225 c. 350 d. 325 Problem 48 The square timber is used as a railroad tie as shown in figure TD-FE014. It carries two uniformly distributed loads of 77 kN each. The reaction from the ground is distributed uniformly over the length of the tie. Determine the smallest allowable dimension b, in mm, if the working stress in shear is 1.0 MPa. Use: a = 0.5 m; b = 0.2 m; c = 1.0 m; a. 180 b. 220 c. 240 d. 310 Problem 49 Find the maximum (simple) span (in m) of a floor joist consisting of a nominal 50 mm by 250 mm coco lumber spaced at 0.6 m on center to carry unfactored dead load of 4.8 kPa and live load 6 kPa. The moisture content is less than 19% max with Fb = 15.37 MPa, Fv = 2.91 MPa, Ew = 3, 663 MPa and deflection limit is span/240 for total load. a. 5.63 b. 4.78 c. 2.64 d. 3.14 Problem 50 See figure TD- FE015. The strut is glued to the horizontal member at surface AB. If the strut has a thickness of 50 mm and the glue can withstand an average shear stress of 1.0 MPa. Use: h = 100 mm; α = 60° Determine the maximum force P that can be applied to the strut, in kN. a. 10.00 b. 11.55 c. 20.00 d. 23.09 W P b A B a A H θ A C L P Fig. TD-FE001 Fig. TD-FE002 5|Page Practice Problems 1 TIMBER DESIGN y h L Fig. TD-FE003 Steel beam A Wood beam t Cable t Wood beam Steel beam h Wooden h post Turnbuckle d B b b Side view Top view Fig. TD-FE004 Fig. TD-FE005 t w h t a b L b Fig. TD-FE006 Fig. TD-FE007 6|Page Practice Problems 1 TIMBER DESIGN truss purlins L rafter L truss ROOF FRAMING PLAN w TRUSS DETAIL Figure TD-FE008 P α C A d B Fig. TD-FE010 Fig. TD-FE012 7|Page Practice Problems 1 TIMBER DESIGN P2 L2 d L1 h P1 θ Structural fiber Steel plate b Figure TD-FE009 Fig. TD-FE011 W d h d L/2 L/2 Fig. TD-FE013 a b c b a b b Fig. TD-FE014 8|Page Practice Problems 1 TIMBER DESIGN P h α A B Fig. TD- FE015 P S2 P Steel rail Wood tie d b Steel (b) girder S1 (a) Fig. TD-FE016 9|Page